28 Electric power – problems and solutions

1. Calculate the electric current of a 10 Watt lamp designed for 12 Volt.

__Known :__

Power (P) = 10 Watt

Voltage (V) = 220 Volt

__Wanted :__ Electric current

__Solution :__

Lamp power = 10 Watt = 10 Joule/second

The equation below shows the relation between the electric power (P), electric potential (V) and electric current (I) stated in formula below :

P = V I

Electric current :

I = P / V = 10 / 220 = 1/22 = 0.045 Ampere

2. Calculate the electric power according to the electric circuit below.

__Known :__

Resistor 1 (R_{1}) = 6 Ω

Resistor 2 (R_{2}) = 6 Ω

Electric voltage (V) = 24 Volt

__Wanted :__ Electric power

__Solution :__

**Equivalent resistor :**

R_{1} and R_{2 }are connected in series. The equivalent resistor :

R = R_{1 }+ R_{2 }= 6 Ω + 6 Ω = 12 Ω

The electric current :

I = V/R = 24/12 = 2 Ampere

Electric power :

P = V I = (24)(2) = 48 Watt = 48 Joule/second

3. Calculate the electric current of a 3 kiloWatt designed for 150 Volt.

__Known :__

Electric power (P) = 3 kiloWatt = 3000 Watt

Electric voltage (V) = 150 Volt

__Wanted :__ Electric current (I)

__Solution :__

Relation of the electric power (P), electric potential (V) and electric current (I) stated in formula below :

P = V I

The electric current :

I = P / V

I = 3000 Watt / 150 Volt

I = 20 Ampere

4. Calculate the power for a \(10\,\Omega\) resistor with a \(5\,A\) current.

Solution: \( P = I^2 R = 5^2 \times 10 = 250\,W \)

5. Determine the power for a circuit with \(12\,V\) and \(4\,\Omega\) resistance.

Solution: \( P = \frac{V^2}{R} = \frac{12^2}{4} = 36\,W \)

6. A \(60\,W\) bulb operates for \(3\,h\). Calculate the energy consumed.

Solution: \( E = Pt = 60 \times 3 = 180\,Wh = 0.18\,kWh \)

7. Calculate the current for a \(200\,W\) appliance on a \(100\,V\) supply.

Solution: \( I = \frac{P}{V} = \frac{200}{100} = 2\,A \)

8. Find the resistance of a heater that uses \(1200\,W\) at \(240\,V\).

Solution: \( R = \frac{V^2}{P} = \frac{240^2}{1200} = 48\,\Omega \)

9. A \(9\,V\) battery is connected to a \(3\,\Omega\) resistor. Find the power dissipated.

Solution: \( P = \frac{V^2}{R} = \frac{9^2}{3} = 27\,W \)

10. Calculate the power in a \(10\,\Omega\) resistor with a \(100\,V\) supply.

Solution: \( P = \frac{V^2}{R} = \frac{100^2}{10} = 1000\,W \)

11. Determine the voltage required to dissipate \(50\,W\) in a \(10\,\Omega\) resistor.

Solution: \( V = \sqrt{PR} = \sqrt{50 \times 10} = 22.36\,V \)

12. A motor uses \(1500\,W\) and runs for \(4\,h\). Find the energy consumed.

Solution: \( E = Pt = 1500 \times 4 = 6000\,Wh = 6\,kWh \)

13. Find the current of a \(240\,V\) supply if the power is \(1200\,W\).

Solution: \( I = \frac{P}{V} = \frac{1200}{240} = 5\,A \)

14. Calculate the resistance for a \(100\,W\) bulb operating at \(200\,V\).

Solution: \( R = \frac{V^2}{P} = \frac{200^2}{100} = 400\,\Omega \)

15. Determine the power in a \(3\,A\) circuit with a \(15\,\Omega\) resistor.

Solution: \( P = I^2 R = 3^2 \times 15 = 135\,W \)

16. Calculate the voltage needed to dissipate \(100\,W\) in a \(20\,\Omega\) resistor.

Solution: \( V = \sqrt{PR} = \sqrt{100 \times 20} = 44.72\,V \)

17. Find the energy consumed by a \(300\,W\) fan running for \(2\,h\).

Solution: \( E = Pt = 300 \times 2 = 600\,Wh = 0.6\,kWh \)

18. Calculate the current in a circuit with \(1000\,W\) power and \(250\,V\) voltage.

Solution: \( I = \frac{P}{V} = \frac{1000}{250} = 4\,A \)

19. Determine the resistance of a \(400\,W\) toaster operating at \(100\,V\).

Solution: \( R = \frac{V^2}{P} = \frac{100^2}{400} = 25\,\Omega \)

20. Find the power for a \(20\,V\) voltage across a \(5\,\Omega\) resistor.

Solution: \( P = \frac{V^2}{R} = \frac{20^2}{5} = 80\,W \)

21. Calculate the voltage needed to provide \(200\,W\) to a \(25\,\Omega\) resistor.

Solution: \( V = \sqrt{PR} = \sqrt{200 \times 25} = 50\,V \)

22. Determine the energy consumed by a \(500\,W\) machine running for \(5\,h\).

Solution: \( E = Pt = 500 \times 5 = 2500\,Wh = 2.5\,kWh \)

23. Find the current for a \(60\,W\) bulb operating at \(120\,V\).

Solution: \( I = \frac{P}{V} = \frac{60}{120} = 0.5\,A \)

24. Calculate the resistance for a \(40\,W\) lamp running at \(20\,V\).

Solution: \( R = \frac{V^2}{P} = \frac{20^2}{40} = 10\,\Omega \)

25. Determine the power in a \(5\,A\) circuit with a \(12\,\Omega\) resistor.

Solution: \( P = I^2 R = 5^2 \times 12 = 300\,W \)

26. Calculate the voltage required to deliver \(150\,W\) to a \(15\,\Omega\) resistor.

Solution: \( V = \sqrt{PR} = \sqrt{150 \times 15} = 61.24\,V \)

27. Find the energy consumed by a \(800\,W\) air conditioner running for \(3\,h\).

Solution: \( E = Pt = 800 \times 3 = 2400\,Wh = 2.4\,kWh \)

28. Determine the current in a circuit with \(500\,W\) power and \(125\,V\) voltage.

Solution: \( I = \frac{P}{V} = \frac{500}{125} = 4\,A \)